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            MERIS Level 1 Radiometric Processor - Radiometric Recalibration Algorithm Specification
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<h3>Algorithm Specification</h3>

<p>The impact of the radiometric calibration changes was assessed by comparing RR products processed with 2nd
    reprocessing and 3rd reprocessing configuration. FR products in 3rd reprocessing configuration were not
    available at time of the analysis. A method was developed to correct 2nd reprocessing Level 1 products
    to 3rd reprocessing quality.</p>

<p>MERIS standard processing algorithms are revised, and as part of this, the degradation model of the calibration
    diffuser has been improved, which results in updated gain values per detector. This is applied in L0 to L1
    processing.
    The Reduced Resolution products are currently undergoing a reprocessing (3rd reprocessing) at ESA;
    however, this applies only to archived RR products, and the Level 1b FRS in use at the MERIS user community
    are at 2nd reprocessing quality. A method has been developed reverting the second reprocessing gains and applying
    the 3rd reprocessing gains, so that TOA radiances are comparable with the 3rd data.</p>

<p>The gains of the 2nd and 3rd reprocessing are taken from MERIS auxiliary files RAC (RAdiometric Calibration) files.
    The RAC files can be found at the following ESA websites:
    <a href="http://earth.eo.esa.int/services/auxiliary_data/meris/_previous/">MERIS Auxiliary Data Files of 2nd
        reprocessing</a>
    <a href="http://earth.eo.esa.int/services/auxiliary_data/meris/">MERIS Auxiliary Data Files of 3nd reprocessing</a>
</p>

<p>The radiometric calibration as described below is a non-linear process including several steps. The radiometric
    gains are the second last step before the L1b are written. However, the last step is the stray light correction
    which is a non-linear process and not revertible from L1b product. The recalibration is therefore only an
    approximation.</p>

<p>The valid MERIS samples are digital counts resulting from the detection and acquisition by MERIS of a bi-dimensional
    field of spectral radiance in front of the instrument. The objective of the radiometric processing, together with
    the stray light correction, is to estimate that spectral radiance. An inverse model of the MERIS processing is used
    for that purpose, using parameters stored in the Characterisation and Radiometric Calibration data bases and the
    MERIS
    samples themselves. The MERIS acquisition model may be described as:</p>

<p align="center"><img src="images/AcquisitionModelEquation.png"></p>

<p>Where</p>
<ul>
    <li><b>m</b> is the camera (or module); <b>b</b> is the spectral band; <b>k</b> is the pixel column; <b>f</b> is a
        frame (processing unit of number of image lines)
    </li>
    <li><b>X<sub>b,k,m,f</sub></b> is the MERIS raw sample</li>
    <li><b>NonLim<sub>b,m</sub></b> is a non-linear function, representing the non-linear transformations which take
        place in the CCD, amplifier and A/D converter; NonLin depends on band and gain settings
    </li>
    <li><b>T<sub>f</sub><sup>VEU</sup></b> is the temperature of the MERIS amplifiers (VEUs) at the time of frame f</li>
    <li><b>T<sub>f</sub><sup>CCD</sup></b> is the temperature of the MERIS detectors (CCDs) at the time of frame f
    <li><b>g</b> and <b>g<sub>c</sub></b> are (dimensionless) temperature correction functions</li>
    <li><b>AL<sub>b,k,m</sub></b> the "absolute radiometric gain" in counts/radiance unit; AL depends on band &amp; gain
        settings
    </li>
    <li><b>L<sub>b,k,m,f</sub></b> the spectral radiance distribution in front of MERIS</li>
    <li><b>Sm<sub>b,k,m,f</sub></b> the smear signal, due to continuous sensing of light by MERIS</li>
    <li><b>C<sup>0</sup><sub>b,k,m</sub></b> the calibrated dark signal (possibly including an on-board compensation),
        dependent on band and gain settings
    </li>
    <li><b>G<b>b,k,m</b></b> a linear operator (weighted sum) representing the stray light contribution to the signal.
        For a given sample, some stray light is expected from all the other samples in the module, spread into the
        sample by specular (ghost image) or scattering processes
    </li>
    <li><b>&epsilon;</b> is a random process representative of the noise and measurement errors</li>
</ul>

<p>This model is inverted during processing: The inverse of the absolute instrument gain ALb,k,m is applied to the valid
    samples of all bands after dark and smear signal subtraction, with a compensation for the estimated temperature
    which is expressed as a function of time:</p>

<p><img src="images/RecalibrationEquation.png"/></p>

<p>Where <b>R<sub>b,k,m,f</sub></b> are the spectral radiances before the straylight correction. The inverse of the
    2nd reprocessing radiometric gains (AL) are multiplied to R, and then the gains of the 3rd reprocessing are
    multiplied to
    give an estimate of the 3rd reprocessing radiances.</p>

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